1. Adding something to xwindows’ auto start
This shoud be easy, in principle. Open autostart and add more lines that start with an ‘@’. Except there are several such autostarts and without knowing which takes priority, it is easy to get frustrated. On my machine there are at least the following:

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/etc/xdg/lxsession/LXDE-pi/autostart

/etc/xdg/lxsession/LXDE/autostart

/etc/xdg/openbox/autostart

/etc/xdg/autostart

/home/pi/.config/lxsession/LXDE-pi/autostart

It is indeed the last one that takes precedence over all others if it happens to exist. So, make changes to that one. Explanation

2. Browser settings for kiosk mode
This should also be easy, just run chromium-browser --help and find the option for kiosk mode. Except it is not there… oops. (Version Chromium 56.0.2924.84). There is an --app option, but it doesn’t result in kiosk mode. Anyways, the option you want is --kiosk (naturally), it’s just that it is an unlisted option and so it doesn’t show up in the help.

In summary, here is the line to add to /home/pi/.config/lxsession/LXDE-pi/autostart

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@/usr/bin/chromium-browser--kiosk http://my.web.site

Lastly you may or may not want to do the following in addition to above (but you’ll have to search for it yourself – there’s plenty of info). They are all optional.